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arXiv 2108.07925quant-ph
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量子测量的序贯乘积

Sequential Products of Quantum Measurements

Stan Gudder

摘要:

我们的基本结构是一个有限维复希尔伯特空间$H$。我们指出$H$上的效应集构成一个凸效应代数。虽然$H$上的算子集也形成凸效应代数,但它们具有更详细的结构。我们介绍了效应和运算的序列乘积。虽然这些已经被研究过,我们引入了新的概念,顺序产品的影响与操作和操作的影响。然后我们考虑各种特殊类型的操作。在发展这些概念的性质后,将结果推广到包括观测量和仪器。特别是,观测量与仪器和仪器与观测量的序列产品的开发。最后,我们考虑条件和共存的观测和仪器。

英文摘要:

Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more detailed structure. W introduce sequential products of effect and operations. Although these have already been studied, we introduce the new concept of sequential products of effects with operations and operations with effects. We then consider various special types of operations. After developing properties of these concepts, the results are generalized to include observables and instruments. In particular, sequential products of observables with instruments and instruments with observables are developed. Finally, we consider conditioning and coexistence of observables and instruments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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